Exploring spatial nonlinearity using additive approximation

Bernoulli

Volumn 13, Issue 2, 2007, Pages 447-472

  Lu, Zudi ^a,b,e   Lundervold, Arvid ^c   Tjøtheim, Dag ^c   Yao, Qiwei ^a,d  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b INSTITUTE OF SYSTEMS SCIENCE   (China)

^c UNIVERSITY OF BERGEN   (Norway)

^d Peking University   (China)

^e CURTIN UNIVERSITY   (Australia)

Author keywords

mixing; Additive approximation; Asymptotic normality; Auto normal specification; Backfitting; Nonparametric kernel estimation; Spatial models; Uniform convergence

Indexed keywords

EID: 42449112095     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ5093     Document Type: Article

References (26)

1. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. Ser. B 36 192-236.
2. Bolthausen, E. (1982). On the central limit theorem for stationary mixing random fields. Ann. Probab. 4 1047-1050.
3. 1 theory. J. Nonparametr. Statist. 6 157-170.
4. Chiles, J.-P. and Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty. New York: Wiley.
5. Cressie, N.A.C. (1993). Statistics for Spatial Data. New York: Wiley.
6. Doukhan, P. (1994). Mixing: Properties and Examples. New York: Springer-Verlag.
7. Diggle, P.J. (1985). A kernel method for smoothing point process data. Appl. Statist. 34 138-147.
8. Diggle, P.J. and Marron, J.S. (1988). Equivalence of smoothing parameter selectors in density and intensity estimation. J. Amer. Statist. Assoc. 83 793-800.
9. Fan, J., Härdle, W. and Mammen, E. (1998). Direct estimation of additive and linear components for high-dimensional data. Ann. Statist. 26 943-971.
10. Gao, J., Lu, Z. and Tjøstheim, D. (2006). Estimation in serniparametric spatial regression. Ann. Statist. 34 1395-1435.
11. Hallin, M., Lu, Z. and Tran, L.T. (2001). Density estimation for spatial linear processes. Bernoulli 7 657-668.
12. 1 theory. J. Multivariate Anal. 88 61-75.
13. Hallin, M., Lu, Z. and Tran, L.T. (2004b). Local linear spatial regression. Ann. Statist. 32 2469-2500.
14. Linton, O. and Nielsen, J.P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82 93-101.
15. Mammen, E., Linton, O. and Nielsen, J. (1999). The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Ann. Statist. 27 1443-1490.
16. Mammen, E. and Park, B.U. (2005). Bandwidth selection for smooth backfitting in additive models. Ann. Statist. 33 1260-1294.
17. Mammen, E. and Park, B.U. (2006). A simple smooth backfitting method for additive models. Ann. Statist. 34 2252-2271.
18. Matheron, G. (1973). Le krigeage disjonctif. Technical Report N-360, Centre de Géostatistique, Fontainebleau, France.
19. Matheron, G. (1976). A simple substitute for conditional expectation: The disjunctive kriging. In M. Guarascio, M. David and C. Huijbregts (eds), Advanced Geostatistic in the Mining Industry NATO Sci. Ser. C Math. Phys. Sci. 24, pp. 221-236. Dordrecht: Kluwer.
20. Newey, W.K. (1994). Kernel estimation of partial means. Econometric Theory 10 233-253.
21. Nielsen, J.P. and Sperlich, S. (2004). Smooth backfitting in practice. J. Roy. Statist. Soc. Ser. B 67 43-61.
22. d: Limit theorems and irregular sets. In M. Moore (ed.), Spatial Statistics: Methodological Aspects and Applications, pp. 57-82. New York: Springer-Verlag.
23. Rivoirard, J. (1994). Introduction to Disjunctive Kriging and Non-linear Geostatistics. Oxford: Clarendon Press.
24. Tjøstheim, D. and Auestad, B. (1994). Nonparametric identification of nonlinear time series: projections. J. Amer Statist. Assoc. 89 1398-1409.
25. Whittle, P. (1954). On stationary processes in the plane. Biometrika 41 434-449.
26. Yao, Q. (2003). Exponential inequalities for spatial processes and uniform convergence rates for density estimation. In H. Zhang and J. Huang (eds), Development of Modern Statistics and Related Topics - In Celebration of Professor Yaoting Zhang's 70th Birthday, pp. 118-128. Singapore: World Scientific.